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Q: What 7 numbers has a range of 10 and a mean of 12?

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four and sixteen16 - 4 = 1216 + 4 = 20 then 20 / 2 = 10Half of 12 is 6, therefore the two numbers 10 - 6 = 4 and 10 + 6 = 16 will have a mean of 10 and a range of 12.Further numbers can be added between 4 and 16 as long as their mean is still 10, eg the data sets:{4, 16}{4, 10, 16}{4, 8, 12, 16}{4, 8, 10, 12, 16}{4, 7, 9, 14, 16}all have a mean of 10 and a range of 12. There is an infinity of such sets.

eight and twelveas mean is 10 then startwith 10 then divide the range of 4 by 2 = 2and take 2 off and add 2 on10 - 2 = 8 and 10 + 2 = 12Check:8 + 12 = 20 then divide those 2 numbers by that 2 so 20 / 2 = 10 mean12 - 8 = 4 range

8, 9, 11 and 12

8 and 12

As there are two numbers, the range is the difference between themAs there are 2 numbers the mean is exactly in the middle of them.Thus half the range is less than the mean and half the range is greater than the mean.Thus the two numbers are 10 ± (4/2) = 10 ± 2 = 8 and 12.Algebraically, this can be seen:Let the two numbers be x and y with y > xThen:their range is y - x = 4; andtheir mean is (x + y) / 2 = 10{2} can be rearrange to give x + y = 10 × 2 → y + x = 20adding {3} to {1} yields: (y + y) + (-x + x) = 20 + 4 → 2y = 24 → y = 12subtracting {1} from {3} yields (y - y) + (x - -x) = 20 - 4 → 2x = 16 → x = 8→ the two numbers are 8 and 12.

Related questions

12 and 8

(10, 12, 12, 13, 13)

Mean: 20.2222222 Median: 12 Mode: 11 Range: 79

four and sixteen16 - 4 = 1216 + 4 = 20 then 20 / 2 = 10Half of 12 is 6, therefore the two numbers 10 - 6 = 4 and 10 + 6 = 16 will have a mean of 10 and a range of 12.Further numbers can be added between 4 and 16 as long as their mean is still 10, eg the data sets:{4, 16}{4, 10, 16}{4, 8, 12, 16}{4, 8, 10, 12, 16}{4, 7, 9, 14, 16}all have a mean of 10 and a range of 12. There is an infinity of such sets.

There is no single answer to that. You could come up with many sets of numbers that would have those properties.

eight and twelveas mean is 10 then startwith 10 then divide the range of 4 by 2 = 2and take 2 off and add 2 on10 - 2 = 8 and 10 + 2 = 12Check:8 + 12 = 20 then divide those 2 numbers by that 2 so 20 / 2 = 10 mean12 - 8 = 4 range

the range is 10

Range = Maximum - Minimum = 20 - 8 = 12.

Mean: 11.6 Median: 12 Mode: 10, 12, 15, 16, 5 Range: 11

One possible set is {9, 9, 10, 11, 12, 15, 18}

8, 9, 11 and 12

8 and 12

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